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Given below are some famous algorithms and some algorithm design paradigms Algorithms Design Paradigm  1. Dijkstra's shortest path algorithms  (a) Greedy design  2. Floyd-Warshall's all-pair-shortest path algorithms  (b) Divide and conquer  3. Kruskal's minimum spanning tree algorithm  (c) Dynamic programming  4. Merge Sort algorithm     Which of the following correspondence is correct?

Given below are some famous algorithms and some algorithm design paradigms Algorithms Design Paradigm  1. Dijkstra's shortest path algorithms  (a) Greedy design  2. Floyd-Warshall's all-pair-shortest path algorithms  (b) Divide and conquer  3. Kruskal's minimum spanning tree algorithm  (c) Dynamic programming  4. Merge Sort algorithm     Which of the following correspondence is correct? Correct Answer 1 - (a), 2 - (c), 3 - (a), 4 - (b)

The correct answer is option 3.

Concept:

Dijkstra's shortest path algorithms:

The greedy approach is used by Dijkstra's Shortest Path algorithm. The shortest path between a given node (referred to as the "source node") and all other nodes in a network is determined by Dijkstra's Algorithm. This approach finds the path that minimizes the total distance (weight) between the source node and all other nodes by using the edge weights.

Dijkstra's shortest path algorithms = (a) Greedy design

Floyd-Warshall's all-pair-shortest path algorithms:

A dynamic programming algorithm, the Floyd-Warshall algorithm is used to solve problems. The Floyd-Warshall algorithm is used to locate all pairs of shortest path issues from a given weighted graph using the all-pair shortest path approach. This approach will provide a matrix that represents the shortest distance between any node and all other nodes in the graph.

Floyd-Warshall's all-pair-shortest path algorithms = (c) Dynamic programming

Kruskal's minimum spanning tree algorithm: 

The greedy method is used by Kruskal's algorithm to find the minimum cost spanning tree. This approach treats the graph as a forest, with each node representing a separate tree. A tree can only link to another tree if it has the lowest cost of all the choices and does not violate the MST characteristics.

Kruskal's minimum spanning tree algorithm=(a) Greedy design

Merge Sort algorithm​:

Merge sort is a divide-and-conquer algorithm based on the principle of breaking down a list into numerous sub-lists until each sub-list has only one element, then merging those sub-lists into a sorted list.

Merge Sort algorithm=  (b) Divide and conquer

Hence the correct answer is 1 - (a), 2 - (c), 3 - (a), 4 - (b).

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